Quantifying Charge Carrier Localization in PBTTT Using Thermoelectric and Spectroscopic Techniques

Chemically doped poly[2,5-bis(3-alkylthiophen-2-yl)thieno[3,2-b]thiophene] (PBTTT) shows promise for many organic electronic applications, but rationalizing its charge transport properties is challenging because conjugated polymers are inhomogeneous, with convoluted optical and solid-state transport properties. Herein, we use the semilocalized transport (SLoT) model to quantify how the charge transport properties of PBTTT change as a function of iron(III) chloride (FeCl3) doping level. We use the SLoT model to calculate fundamental transport parameters, including the carrier density needed for metal-like electrical conductivities and the position of the Fermi energy level with respect to the transport edge. We then contextualize these parameters with other polymer-dopant systems and previous PBTTT reports. Additionally, we use grazing incidence wide-angle X-ray scattering and spectroscopic ellipsometry techniques to better characterize inhomogeneity in PBTTT. Our analyses indicate that PBTTT obtains high electrical conductivities due to its quickly rising reduced Fermi energy level, and this rise is afforded by its locally high carrier densities in highly ordered microdomains. Ultimately, this report sets a benchmark for comparing transport properties across polymer-dopant-processing systems.

Molecular weight information was collected on a Tosoh ECOSEC High-Temperature GPC using 1,2,4trichlorobenzene as the elutent at 140 °C. Results are relative to narrow molecular weight polystyrene standards. As the PBTTT sample dissolves well when heated, as seen by a light orange solution compared to the arrogated purple solution at RT, and the GPC trace show no unusual peak shape, we expect the high Mn measured is accurate and not the result of arrogation.
Electrochemistry: Electrochemical measurements (CV and DPV) were performed using a model 273A EG&G PAR potentiostat/galvanostatic controlled by CorrWare. The electrical potential in the threeelectrode cell setup was measured using a Ag/AgCl reference electrode (potentials reported relative to the ferrocene ferrocenium redox couple, as measured using this setup). TBAPF6 (recrystallized from ethanol) was used as the supporting electrolyte (0.5 M in propylene carbonate) and a platinum flag was used as the counter electrode. Films were prepared by drop casting 1 µL of a 8 mg/mL solution of PBTTT in hot chlorobenzene onto a glassy carbon button electrode (area = 0.07 cm 2 ). Ionization potentials were measured by differential pulse voltammetry (DPV) on a freshly processed film, giving an onset at +0.19 V versus ferrocene/ferrocenium which correlates to an IP of 5.29 eV. This calculation assumes that ferrocene has an onset of oxidation of -5.1 eV, 3 and that DPV measured and calculated values are commensurate to solid-state properties. 4 Differential Scanning Calorimetry: DSC measurements were performed on TA Instruments DSC250 Differential Scanning Calorimeter using Tzero pans and a measurement range from to using a rate of 10 °C /min. Two samples of PBTTT-C12 of approximately 4 mg each were prepared for calorimetry by first dissolving the polymer in chlorobenzene at a concentration of 10 mg/mL, heating the solution for 1 hour at 80 °C, then drop-casting the solution onto clean glass substrates with a substrate temperature of 80 °C.
One of these 4 mg samples, denoted as the "as cast" sample, was measured as a reference for the PBTTT-C12 polymer (see Figure S4a). The as-cast sample shows two well-defined endotherm melting peaks with onset temperatures of 170 °C and 260 °C and complementary exotherms with onset temperatures of 140 °C and 260 °C. These thermal transitions are often ascribed to side-chain and backbone chain melting, respectively. Depending on the literature reference, these strong endotherms for PBTTT-C12 can be consistent 2, 5 or inconsistent 2, 5, 6 with previous reports on PBTTT derivatives (including PBTTT-C12).
After this first experiment was conducted, denoted as "exp.1," the sample was subsequently re-solvated, re-processed as described earlier, and re-measured (see "exp. 2") to determine if the DSC measurement altered the chemical structure or degraded the material. The thermograms in Figure S4a and Figure S4b are nearly identical, indicating that this DSC procedure does not affect the inherent chemical structure of the PBTTT-C12 reported herein.
The second drop-casted sample was thermally annealed similar to wire-bar films by placing the drop-casted films onto a hot plate at 180 °C for 20 minutes under dark and ambient atmosphere. This thermally annealed sample was measured as a reference for quantifying the effects of thermal annealing on polymer structure, used for the report thermoelectric, GIWAXS, and SE measurements. Relative to the as-cast samples, Figure  S4c shows that thermally annealing PBTTT-C12 decreases the enthalpic peak area and intensity with respect to the as cast films. This decrease in enthalpic peak area suggests that thermal annealing PBTTT-C12 inhibits thermal transitions for the PBTTT-C12 reported in this study. This enthalpic inhibition indicates that there is less crystalline material to melt at these temperatures. Although we cannot robustly claim to what extent which mechanism is responsible for this decrease in DSC endotherms after annealing, we note that the C-1s and S-2p XPS spectra for PBTTT-C12, after wire-bar coating and annealing, is akin to many other alkyl thiophenes; therefore, XPS data suggests that this annealing process does not significantly oxidize or chemically degrade the PBTTT-C12 surface. Additionally, we note that GIWAXS diffractograms for PBTTT-C12, after wire-bar coating and annealing, show strong diffraction peaks (multiple order reflections and low paracrystallinity values); therefore, GIWAXS data suggests that this annealing process does not completely remove all ordering in the PBTTT-C12 reported herein. We note that there are several studies that report on PBTTT derivatives (including -C12) that have small and diffuse DSC melting endotherms but rather prominent GIWAXS peak signal. 2,[5][6][7] Film Preparation: A 10 mg/mL solution of PBTTT in chlorobenzene was heated to 80 °C for one hour. Before coating, Au contact pads (150 nm thick, 5 mm apart, arranged in a van der Pauw geometry) were evaporated onto cleaned microscope slides with a 5 nm titanium adhesion layer underneath. Glass slides were cleaned before Au deposition and before film coating by sonicating in acetone (5 min), followed by isopropyl alcohol (5 min), drying with N2 and treating with ultraviolet-ozone (5 min). Then, the prepared solution (60 µl) was cast onto a 7.6 cm × 2.5 cm glass slide and wire bar coated at approximately 180 mm s −1 using a substrate temperature of 80 °C on a K Control Coater with a close-wound wire diameter of 0.3 mm. After coating, thin-film samples were prepared by carefully cutting the 7.6 cm × 2.5 cm film into 1 cm × 1 cm squares. After film preparation, PBTTT films were thermally annealed at ca. 180 C for 20 S5 minutes in the dark and under ambient atmosphere. 8 Films were then cooled to room temperature by turning off the hot plate.
Doping Procedure: A 50 mM solution of FeCl3·6 H2O (Alfa Aesar, 97%) in acetonitrile (99.8%, Sigma Aldrich) was prepared and then serially diluted with acetonitrile to the desired doping concentration. To dope the films, 50 L of the FeCl3 dopant solution was dropped onto a ~ 1 cm 2 film. The dopant solution soaked the film for three minutes and was coved by a glass Petrie dish to mitigate solvent evaporation. After three minutes, the dopant solution was pipetted off, and the film was then rinsed with excess acetonitrile (> 100 L). Excess solvent was removed via vacuum drying for three minutes at ~ 1 Torr and room temperature.
Thermoelectric Measurements: Thermoelectric measurements were performed immediately after doping to mitigate the effects of ambient atmosphere and time on the resulting thermoelectric properties. 9 Electrical conductivity and Seebeck coefficient measurements were performed on a custom set up, using temperaturecontrolled Peltier units and tungsten tipped micromanipulators. Electrical conductivity measurements were performed using the Van der Pauw technique on top of a single Peltier unit. The micromanipulators made electrical contact by piercing through the PBTTT films to the bottom gold contact pads, spaced ca. 5 mm from one another. For temperature dependent measurements, the electrical conductivity was measured from ca. 15 C to 35 C in steps of 2.5 C to mitigate thermal degradation and calculate the activation energy in the vicinity of the nominal ( ) values reported in the main text. The Seebeck coefficient was measured by suspending the film between two Peltier stages and applying a series of temperature gradients (up to Δ = 5 C, centered about the central temperature) across the film. The resulting thermoelectric voltage was measured across two gold contact pads, and the temperature of each contact pads was measured using Ktype thermocouples. The Seebeck coefficient was calculated from the slope of the thermoelectric voltage as a function of the applied Δ . Over this doping ranges and temperature range, ca. 15 C to 35 C, Seebeck coefficients were temperature independent. All measurements were captured using a Keithley 2700 DMM and a 7708 Mux card via a LabView interface. Film thicknesses were measured using a ProFilm optical profilometry by measure the step height across a small scratch in the film after the doping and thermoelectric measurements steps.
UV-Vis-NIR Measurements: An Avantes fiber optic spectrometer (Avaspec-ULS2048CL-EVO-RS) with a deuterium-tungsten, halogen light source (Mikropack DH-2000) was used in transmission mode to collect ultraviolet-visible-near infrared (UV-vis-NIR) optical measurements on glass substrates immediately after doping. Film thicknesses were measured using a ProFilm optical profilometry by measure the step height across a small scratch in the film. Thickness values were needed to calculate the attenuation coefficient values in Figure 1b.
GIWAXS Measurements: PBTTT films were deposited on undoped Si wafers with a native oxide layer, akin to previously described. Films were measured at Soft Matter Interfaces Beamline (SMI, Beamline 12-ID) at the National Synchrotron Light Source II at 12 keV. X-ray scattering patterns were recorded on a Pilatus 900 K−W detector, consisting of 0.172 mm square pixels, mounted at a fixed distance of 0.279 m from the sample position. To cover the range of scattering angles desired, the vertically oriented elongated detector was moved horizontally on a fixed arc and images were later visualized in Xi-CAM software 10 and stitched using custom code. The sample and detector were enclosed in a vacuum chamber to suppress air scatter. Scattering patterns were measured as a function of angle of incidence, with data shown acquired with an angle of incidence near the critical angle that maximized scattering intensity from the sample.
Spectroscopic Ellipsometry (SE) Measurements: SE measurements were performed on a Woollam Alpha-SE ellipsometer at an incident angle of 70 o and analyzed using CompleteEASE software. Scotch tape was adhered to the backside of the glass substrate to mitigate multiple reflections between the substrate, film, S6 and metal sample stage. A Cauchy model for the bare glass substrate with scotch tape (no PBTTT film) was developed and then used for subsequent modeling.

Note S2: UV-Vis-NIR Peak Deconvolution for Carrier Concentration Calculations
UV-Vis-NIR measurements on PBTTT thin films were measured in transmission mode. The percentage of transmission (% ) is defined as the ratio of the attenuation of light intensity due to the film ( ( ) 0 ( ) × 100%) and was converted to absorbance ( ), using Beer-Lambert law, = 2 − log 10 (% ). The absorbance of a film is a function of the concentration ( ), extinction coefficient ( ), and path length ( ) ( = ), and the path length is equal to the film thickness in this experimental set up.

Figure 2b
plots the measured absorbance normalized by the measured film thickness ( ) in units of cm -1 for each doping level, and this is defined as the attenuation coefficient. We calculate that value of the attenuation coefficient for pristine PBTTT, 0.7 x 10 5 cm -1 , is comparable to other pristine conjugated polymers when measured using this method. [11][12][13] Note that these attenuation coefficients were performed using transmission mode UV-Vis-NIR with log-based-10 procedures. These methods and formalisms are not necessarily consistent with those used with ellipsometry. Oftentimes with ellipsometry, the reflectance, absorption, and transmission contributions are accounted (via the changes in the reflected polarized light phase and intensity) and natural logarithms (log-based-) are used.
PBTTT doped with FeCl3 has FeCl4counteranions. 8 If each polaronic charge carrier has a single counteranion, and these counteranions have a fixed charge and molecular stoichiometry, then the FeCl4absorbances at ca. 3.4 and 3.9 eV can be used to quantify the concentration of FeCl 4and polaronic charge with respect to the concentration of BTTT monomers. An extinction coefficient of 50,000 L mol -1 cm -1 for PBTTT was used 12 in conjunction with the pristine PBTTT film thickness and absorbance to define the concentration of BTTT monomers in the films (see Note S1 of Ref. 13 ). Extinction coefficients of 8,100 and 7,400 L mol -1 cm -1 for the 3.4 and 3.9 eV peaks of FeCl4were used, respectively (see Table S4 of Ref. 8 ). 8 These FeCl4extinction coefficients were used in conjunction with the deconvolved attenuation coefficient peak heights to calculate the FeCl4concentrations. Peak deconvolutions were necessary because the peak shape and baseline shifted as a function of doping level. 8,14 At each doping level, the peak height was calculated using a mixed Gaussian-Lorentzian peak deconvolution using Origin 2021 software. Figure S5,6 shows representative deconvolutions.
The calculated molar ratios of FeCl4with respect to PBTTT ranged from 0.11 to 0.40, and these molar ratios are comparable to previous reports. 8,14 Carrier ratios were calculated by assuming that each PBTTT repeat unit can support two charge carriers (i.e. two carriers repeat unit). 15 Carrier densities were calculated using a repeat unit molecular weight of 694.8 g mol -1 and a mass density of 1.1 g cm -1 . 12 By using two FeCl4peaks for deconvolution, uncertainty error bars are provided and represent the standard deviation of the two deconvoluted peaks. This molar ratio uncertainty was propagated to carrier ratios and carrier densities in the SLoT analysis. S12 Figure S5: UV-Vis-NIR spectra used for FeCl4peak deconvolution.

S14
Note S3: SLoT modeling notes Figure S7 shows the XPS measurements and deconvolutions for PBTTT doped with FeCl3 at varying molarities. All deconvolutions show a low 2 value and Abbe criterion, indicating that these deconvolutions are statistically significant and can be representative of the measured data. The pristine spectra was first deconvoluted, with a single sulfur 2p doublet, using a fixed S 2p3/2 : S 2p1/2 area ratio of ~0.511 and a peak binding energy separation of ~1.2 eV, consistent with previous studies and standards. [16][17][18] The 0.88 mM doped film has a comparable S 2p signal to the pristine film, so a second S 2p doublet could not be prudently incorporated. Therefore the 0.88 mM film does not have an extent of oxidation that can be reasonably quantified and deconvoluted using XPS; this is in stark contrast to all thermoelectric and optical measurements which clearly show evidence of oxidation.
At 2.5 mM and 50 mM, XPS measurements notably and asymmetrically shift towards higher binding energies, indicative of oxidative doping. Because of binding energy and area ratio constraints, a second set of doublet peaks are needed to capture the signal at higher binding energies. The area of these oxidized doublets with respect to the total sulfur area is used to quantify the extent of sulfur oxidation. At 2.5 mM, the oxidized sulfur : total sulfur area ratio is 0.09 or ~1 out of 10 sulfurs are oxidized. At 50 mM, the oxidized sulfur: total sulfur area is 0.24, or ~1 out of 4 sulfurs are oxidized. With 4 sulfurs per monomer unit, these XPS results are commensurate with a dopant : monomer ratio of 0.36 and 0.96, respectively, and a carrier ratio of 0.18 and 0.48 (assuming 2 sites per monomer), respectively. For reference, the UV-Vis-NIR peak deconvolutions yielded carrier ratios of 0.22 ± 0.06 and 0.40 ± 0.04, which is consistent within error of the XPS measurements. Additionally, we note that XPS survey measurements and elemental spectra for iron and chlorine substantiate the use UV-Vis for FeClx concentration quantification ( Figure S8, Table  S1). Notably, PBTTT having a maximum extent of doping of 1 out of 4 sulfurs oxidized is still low compared to P3HT (~1 out of 3) and PE2/PEDOT (~ 1 out of 2), 16,19 and an order of magnitude lower than that modeled used spectroscopic ellipsometry or AC Hall effects. 14 We also note that the intensity-weighted average binding energy ( W ) shifts are reasonable and consistent with the values calculated using the SLoT model. If the reference vacuum energy level is constant, and the shift in core energies is equal to the shift in valence energies (as shown in Ref. 18  , where the bounds of 2 and 1 are the binding energy bounds (ca. 161 and 168 eV for S-2p in this study). Similarly, if the transport edge is constant and the transport properties are well modeled using a linear transport function, then the shift in is commensurate to the shift in F . Explicitly, at 0.88 mM, the w is 164.36 eV with an of 1.5. At 50 mM, the w is 164.67 eV and of 14. Therefore, as the extent of doping increases from 0.88 mM to 50 mM, the Δ = 0.31 eV and the Δ = 12.5 = 0.33 eV at 300 K. Because Δ w ~ Δ , we assert that the asserted transport function (and its localized prefactor, see Eq. 1-3) are reasonable and self-consistent with the spectroscopic observations. Figure S9a shows that 0 does not have a statically significant linear slope (p-score > 0.05) and therefore does not significantly vary as a function of doping level. This invariance is in stark contrast to E 0 which shows an exponential dependence on doping level and reinforces the need to quantify H . Therefore, we assert that 0 can be used to describe the entire PBTTT-FeCl3 series studied herein. A single 0 parameter is useful because it quantifies the propensity for high electrical conductivities and mobilities for a system, independent of doping level, and it can be related to energy-independent contributions to charge transport (e.g. effective mass in a parabolic band approximation). 20 Because 0 is constant, we examine the distribution of 0 values calculated for each film. Each films' 0 is represented by a single small black box in Figure S9b. The large grey box represents the average value ± one standard deviation, and whiskers represent two standard deviations. The star represents the median value, and a simple Gaussian curve is overlayed. Asserting that 0 = 25 S cm -1 is consistent with the distribution shown in Figure S9b, fits the experimental ( ) curve (with the asserted H ( ) and ( ) curves), and is consistent with our previous predictions. 16 Figure S10 shows our previous models and predictions regarding charge transport in chemically doped PBTTT. The SLoT model parameters used for the predicted curves are found in Ref. 16 , the PBTTTC14 data is found in Ref. 15 , and the PBTTTC16 data is found in Ref. 21 . From these literature reports, we previously predicted the 0 and SLoT curve from solely ( ) data. Here we fully evaluated the SLoT model and found consistency with our previous model predictions.  . (a,b,e,f) measured and deconvoluted spectrograms. (c,d,g,h) calculated fitting errors as calculated from residuals/ envelope x 100% S17 Figure S8: X-ray photo electron spectroscopy measurements for (a) chlorine and (b) iron. Vertical axes are offset to facilitate comparisons between spectra.

S19
Note S4: GIWAXS Figure S11 shows a representative peak assignment from a radially integrated GIWAXS pattern. Peaks were deconvoluted using Origin 2021 software, with an asymmetric least squares background fit and a Lorentzian-Gaussian cross peak shape.
Two common tools to analyze the size and quality of a crystalline domain in conjugated polymers are the coherence length ( c ) and paracrystallinity ( ). 7,[22][23][24] Oftentimes, the coherence length can be calculated using the Scherrer equation ( c = 2 Δ ), where is a shape factor (near 0.9), and Δ is the full width at half-max (FWHM) in -space for a diffraction peak. 22 This Scherrer equation is best used for inorganic crystalline materials that do not have disorder, where the peak width is only affected by the crystal size. In these ideal crystalline systems, the FWHM is nearly constant for all higher order reflections, e.g. (200), (300), etc. In contrast, semiconducting polymers have cumulative disorder (predominantly paracrystalline disorder). With cumulative disorder the polymer chains have an increasing propensity to change spatial coordinate and lose periodicity. Therefore, as the reflection order increases, the FWHM increases, as shown in Figure S12a.
To isolate the effects of paracrystalline disorder on the (h00) lamellar peak, the FWHM is plotted as a function of h 2 , and c is the calculated y-intercept. At the y-intercept, the effects of disorder are minimized (mathematically, this can be thought as a zero-order reflection). Figure S12b shows that as h 2 increases, the FWHM increases linearly. Note that a (400) peak was not deconvoluted for the 50 mM PBTTT film, as the (400) peak was not isolatable from (003) peak.

Table S2
shows the c values calculated using simple Scherrer equation with the (100) peak and the c values calculated using the linear intercept method. Both methods show that doping decreases c in the (h00) direction, consistent with previous reports. 25 Furthermore, we note that when performing linear regressions, it is important to report the range of the confidence interval (or some error approximation) and the statistical significance (p-score). Here, we find that the p-score for the intercept is greater than the confidence level (0.05) in most films. Therefore, there is a large degree of uncertainty around c values reported using the linear intercept, i.e. statistically insignificant. This is also reflected in the large range of permissible values within the 95% confidence intervals (CI). This statistical analysis weakens the argument that doping affects c , as calculated using the intercept method.
Regarding the (110) peak, for the − stacks, the paracrystallinity values is oftentimes reported because higher order (ℎ10) peaks are not oftentimes observable, making the intercept method unusable. Additionally, we note that we attribute this peak to the (110) Miller index, and not (010) because PBTTT has a triclinic unit cell. 26 It can be shown for highly disordered systems that = 1 2 √Δ • , where is the real spacing of the (110) peak; note that this equation assumes that the effects from lattice-parameter fluctuation can be neglected. 23 For context, values range for highly crystalline small organic molecules (pentacene, ~ 5%) well-ordered conjugated polymers (PBTTT/P3HT, ~ 5-15%), disordered conjugated polymers (PCDTBT , ~ 15-25%) and amorphous (PMMA, , > 25%) 7 We find that the value of this PBTTT is quite small, ca. 5.5 %, which indicates high ordering within the crystalline domains.    Figure S13 shows the spectroscopic ellipsometry measurements. Note that all and axes are the same scaling to help comparisons, but individual films ranged from ca. 60 to 250 nm which can affect the observed and . Measured data points are represented by hollow data points and only every fifth data point is shown for clarity. Solid lines represent B-spline model fits, calculated using an optical model. This optical model was developed using known film thicknesses (measured using optical profilometry) and known glass substrate optical properties (measured using ellipsometry). The B-spline model fits assumed Kramers-Kronig consistency. This optical model was developed using the CompleteEASE software (J.A. Woollam). Figure S14 shows the calculated ̃,̃, and values. ̃ is the real part of the index of refraction, ̃ is the imaginary part of the index of refraction, and is the absorption coefficient. We use tilde (~) above and here to distinguish the index of refraction values from carrier densities and wave vectors. These values are related to 1 and 2 , 27

S21
(S2) The pristine − * transition obtaining a maximum ̃ value near 3 is consistent with literature reports on conjugated polymers. 28,29 Additionally, pristine PBTTT obtaining a maximum ̃ value near 1.5 is consistent with previous reports. 28 Notably, it has been shown that the complex index of refraction increases significantly with increasing molecular weight in conjugated polymers. 28 The absorption coefficient, is calculated as, 28,30 where is the wavelength. Absorption coefficients ought to be asserted only when contributions from reflection, transmission, and absorbance are measurable and/or calculable. For example, transmission UV-Vis-NIR measurements alone may not be able to assert values because the reflectance is not measured, and the commonly reported absorbance assumes that all light is either absorbed or transmitted. In contrast, spectroscopic ellipsometry uses the changes in reflected light intensity and phase of s-and p-polarized light in a system of equations. 27 These nuanced differences in measurement is why in Figure 2 we asserted attenuation coefficients while in Figure S14 we asserted absorption coefficients ( ). Furthermore, the absorption coefficient is calculated from measured intensities using natural logarithms (i.e. ( ) = 0 exp(− )). These subtle differences undermine the importance of clearly reporting optical measurement conditions and assumptions and to judiciously make fair comparisons between comparably obtained values.
In a series of electropolymerized dioxythiophene derivatives, measured using both reflectance and transmission measurements, for the pristine − * peak near 2-2.2 eV ranges from 1.5 -2 x 10 5 cm -1 . 31,32 In a series of thieno[3,2-b]thiophene-diketopyrrolopyrrole (DPP-TT-T) polymers measured using spectroscopic ellipsometry, for the pristine − * peak near 1.5-2 eV ranges from 2.2 -3 x 10 5 cm -1 . 28 Notably, in Ref. 28 , the authors found that polymers with long, colinear, planar monomers have enhanced values. Lastly, we note that for this PBTTT system, the amount of paracrystalline disorder is exceptionally low (~ 5.5 %), 7 which indicates comparatively high levels of ordering in the − stacks, and this could be responsible for the large values. Considering these literature comparisons and the additional characterizations performed herein, we believe that the calculated ̃,̃, and values are reasonable. Figure S15 shows the 2 deconvolutions for the 50 mM FeCl3 doped PBTTT films. The deconvolution with the Drude contribution has a mean squared error (MSE) of 3.4. The deconvolution without the Drude contribution, has a MSE of 13.9. This suggests that the Drude contribution improves the model fitting. Qualitatively, it is seen that the model fitting without the Drude contribution has steeper slopes and larger amplitudes for the polaronic and − * transitions. A Drude-like asymptotic tail reduces these effects. Figure S16 shows the attenuation coefficient and approximated imaginary part of the refractive index. Note that these measurements were performed using attenuated total reflectance-infrared spectroscopy (ATR-FTIR), with no complimentary transmission or reflectance measurements. Therefore, we caution precise quantitative comparisons in these IR spectra, but encourage semi-quantitative and qualitative analysis. FTIR-ATR measurements were performed on a Thermo Fisher Scientific Nicolet iS5 FTIR with an iD7 Diamond ATR attachment. Before each measurement, background scans were collected on an empty ATR stage and software subtracted from the measured spectrum. PBTTT films were measured on glass slides by placing the film side "face down" onto the ATR crystal and mechanical pressure was applied to ensure contact between the film and ATR crystal. Films were sufficiently thin so that the ATR measurement measured the through the film thickness.
In Figure 16a, the attenuation coefficients are reasonable and within a factor of 2 of the absorption coefficient ( ) reported for XDOT derivatives using both transmission and reflectance techniques. 31,32 Furthermore, these attenuation coefficients at 0.6 eV are approximately equal to those at 1.4 eV measured using spectroscopic ellipsometry. The pristine spectra show CHx absorbances (near 3000 cm -1 ) associated with the hydrocarbon sidechains in PBTTT. These CHx peaks are observable across most doping levels, but a Drude-like and/or (bi)polaronic band emerges in the mid-infrared (MIR) that obfuscates these peaks at higher doping levels. As polaronic charge carriers become more delocalized and mobile, a broad MIR peak (between 0.2 and 1 eV) emerges and shifts to lower energies (associated with intrachain transport), and the peak at 0.17 eV (associated with interchain transport) increases in amplitude with respect to the interchain peak. 33,34 Initially, the intrachain MIR peak redshifts and the interchain peak increases in amplitude with respect to the MIR peak (ca. pristine through 1.25 mM). Beyond 1.25 mM, these polaronic trends are not consistent with the experimental observations. The attenuation coefficients continue to broaden into linear slopes as the molarity increases from 1.25 mM to 50 mM. Notably, the transition at ca. 1.25 mM is at the same molarity where H < B and the SLoT model becomes co-linear with the delocalized model (Figure 3d). Figure 16a are Drude model curves which show absorbance due to free carriers. Notably, these Drude model curves cannot capture the discrete oscillatory transition associated with the CHx absorbances, and the inter/intrachain polaronic absorbances. Indeed, Lorentz-like oscillators are needed for these transitions. However, these Drude model curves can help explain the slopes and curvatures exhibited by the 1.25 mM through 50 mM curves.

Also shown in
The bottom most model curve, 3 x 10 20 carriers cm -3 , was calculated using the macroscopic transport parameters. The slopes and curvatures of this model are inconsistent with the spectroscopic measurements and indicate that the macroscopic transport measurements are an underestimate of the transport properties in the most conductive domains. The topmost curve, 6×10 21 carriers cm -3 , was calculated with the transport S24 parameters from spectroscopic ellipsometry, in the range of 1.4 to 3.2 eV. Here, we observe that the slope and curvature may be too steep to explain the MIR optical properties. This could be because of the ATR-FTIR set up and/or because the ellipsometry measurements were performed in too narrow of a spectroscopic range. Lastly, we model a middle curve, with averaged electrical conductivities and carrier densities from the other two curves. We find that this middle curve fits the 2.5 mM spectrum exceptionally well and may be a basis for explaining the other highly doped curves.
Overall, these MIR optical measurements and models confirm that there is a Drude contribution, especially at higher doping levels, and there are likely domains with higher carrier densities and electrical conductivities than observable with macroscopic transport measurements. Ultimately, performing spectroscopic ellipsometry over wider frequency ranges, more angles, and with additional polymeric systems is needed.